Method for determining the function representing the effect of non-reciprocity of a radiographic film

ABSTRACT

The invention relates to radiology systems and, more particularly in such systems, to a method that enables the effect of non-reciprocity of the radiographic film to be determined. This effect of non-reciprocity is expressed by coefficients CNRD(d i ) which are a function of the photon dose rate (d i ) on the film, the coefficients CNRD(d i ) being obtained from the coefficients CNRT(t i ) and the determination of the reference lumination L ref  received by the film.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The invention relates to radiology systems using a radiological filmand, more particularly in such systems, to a method by which the effectof non-reciprocity of the radiographic film can be determined.

2. Description of the Prior Art

A radiology system essentially comprises an X-ray tube and a receiver ofX-radiation, between which the object to be examined, for example a partof a patient's body, is interposed. The image receiver which is, forexample, a film/screen couple, gives an image of the object after anappropriate exposure time and the development of the film. For the imageof the object to be used as efficiently as possible, the different dotsthat constitute it should have sufficient contrast with respect to oneanother, namely, the blackening of the radiographic film should beappropriate, from one radiographic shot to the next one, despite thepossible differences in opacity of the radiographed object.

The blackening of the film is related to the quantity of energy of theradiation incident on the film/screen couple, namely, the product of theintensity of the radiation to which the radiographic film is subjected,or "film" dose rate, by the time during which the film is exposed tothis radiation. Consequently, to obtain a constant blackening of thefilm from one radiography to another, there is a known way of makingmeasurements, during the examination, of the incident energy on the filmby means of a detection cell, generally placed before the receiver, thatis sensitive to X-radiation and gives a current proportional to the"film" dose rate. This current is integrated, from the start of theexposure, into an integrator circuit that gives an increasing valueduring the exposure. This increasing value is compared, during theexposure time, with a fixed reference value, established beforehand as afunction of the characteristics of the film. The end of the exposuretime is determined by the instant at which the comparison indicates thatthe value representing the incident energy on the film is equal to thereference value.

Should the radiographic film be directly subjected to X-radiation, andshould the variation in the exposure times from one examination toanother be small enough, a constant blackening of the film is obtainedfrom one exposure to the next one, independently of the duration of theexposure time S, provided that the product of the exposure time S by thedose rate F is constant, i.e. the value resulting from the integrationshould remain constant.

This is true only if the characteristics of the film obey the law ofreciprocity which indicates that the optical density of the film isproportional to the product F×S and if the response of the film isindependent of the quality of the incident X-ray beam. This law ofreciprocity is no longer met when the variation in the exposure times isgreat.

Besides, should the radiographic film be associated with an intensifyingscreen, the blackening of the film will depend on the quality of thespectrum. For, the response of the screen depends on the energydistribution of the spectrum of the radiation received, which means thatit is sensitive to the hardening of the spectrum and to the change involtage of the X-ray tube. Finally, there are certain applicationswherein it is costly for the detection cell to be placed before the film(for example in mammography), for the radiation energy is such that thedetection cell would then be visible on the film. In this case, it isplaced behind the image receiver but this creates an additionaldifficulty for the signal received by the detector cell is the one thathas not contributed to the blackening of the film. The result thereof isthat the measurement made by the detection cell does not generallyrepresent the incident "lumination" (.i.e. the quantity of lightreceived multiplied by the exposure time) on the radiographic film.

The deviation from the law of reciprocity, which varies according to thetype of film, represents the relative variation of the lumination neededto obtain a constant optical density when the exposure time S varieswhile the spectrum of the X-radiation is constant. This is expressed bythe fact that, to obtain a same optical density of the film, thelumination should be, for example 1 for an exposure time S=0.1 second,1.3 for S=1 second and 2 for S=4 seconds.

This deviation from the law of reciprocity is due to the phenomenonknown as the Schwarzschild effect. This effect is described notably inthe work by Pierre GLAFKIDES, CHIMIE ET PHYSIQUE PHOTOGRAPHIQUES(Photographic Chemistry And Physics), 4th edition, pages 234 to 238,PUBLICATIONS PHOTO-CINEMA Paul MONTEL.

To take account of this deviation from the law of reciprocity, variousapproaches have been proposed, and one of them has been described in theFrench patent No. 2 584 504. This patent proposes the comparison of theintegrated value of the signal given by the detection cell with areference value that varies during the exposure according to adetermined relationship. More precisely, from the start of each exposureperiod, an additional value is added to the difference between thevalues of the integrated signal and of the reference value. Thisadditional value increases as a function of time according to apreviously determined relationship, for example an exponentialrelationship.

This previously determined relationship, whether it is exponential orotherwise, takes account of the deviation from the law of reciprocityonly in an imperfect way. In particular, it does not take account of thevariations in the luminous intensity effectively received by the film.Furthermore, this correction does not take account of the effects ofother phenomena such as the hardening of the X-radiation due to thethickness of the object crossed or the modification of the spectrum dueto the voltage of the X-ray tube.

Furthermore, in this method, the detection cell is placed before theimage receiver.

Another approach, which takes account of the different effects that comeinto play, notably the variations in the tube current, the hardening ofthe spectrum due to the thickness of the object crossed, themodification of the spectrum due the voltage of the tube and, when anintensifier screen is present, the absorption response of said screen,has been described in U.S. Pat. No. 5,218,625.

In this method, to take account of the variations of the current of theX-ray tube and, more generally, of the variations of the dose rate ofphotons on the radiographic film, a non-reciprocity coefficient CNRD isused, expressed in the photon dose rate incident on the film, byparticular measurements and computations.

The object of the present invention, therefore, is to implement a methodfor the determination of the function representing the effect ofnon-reciprocity of a radiographic film expressed as a function of thephoton dose rate on the radiographic film.

SUMMARY OF THE INVENTION

The invention relates to a method for determining the functionrepresenting the effect of non-reciprocity of a radiographic film in asystem of radiology designed to examine an object that includes an X-raytube, the supply voltage of which may assume various values V_(m), withcontinuous or discrete variation, said X-ray tube emitting an X-ray beamin the form of pulses of variable duration t_(i) towards the object tobe examined, an image-receiver of the X-radiation that has crossed theobject to form an image of said object, an X-ray detection cell thatenables the conversion of a physical variable, characterizing the X-raybeam, into a measurement signal L, an integrator circuit that integratesthe measurement signal L for the duration t_(i) and gives a signal M,and a device to compute the yield D given by the ratio of M to theproduct I×t_(i) of the anode current I of the tube by the duration t_(i)of the exposure, wherein said method includes the following steps of (oroperations for):

(a) determining the coefficients of non-reciprocity CNRT(t_(i)) of thefilm expressed in exposure time t_(i) for an optical density DO_(refo)of the film;

(b) determining a reference lumination L_(ref) received by said film,

(c) calculating photon dose rates d_(i) on said film by the formula:##EQU1## (d) determining the coefficients of non-reciprocity CNRD(d_(i)) expressed in photon dose rate d_(i) by the application of theformula:

    CNRD (d.sub.i)=CNRT (t.sub.i)                              (19)

said coefficients CNRD (d_(i)) being modelized according to a functionsuch that:

    CNRD=(d)=A'.sub.0 +A'.sub.1 log 1/d+A'.sub.2 [log 1/d].sup.2( 20)

The step (a) of the method may also comprise the following steps of:

(a₁) modifying the tube heating current so as to obtain different valuesof said current,

(a₂) reading values M (t_(i)) given by the integrator circuit fordifferent exposure times (t_(i)) so as to obtain an optical density DO₁of the film

(a₃) calculating the ratio ##EQU2## which gives the coefficient CNRT(t_(i)) with M (t_(ref)) the value M (t_(i)) for t_(i) =t_(ref)

The step (a) of the method may also be achieved by the following stepsof:

(g1) making, by means of a variable time sensitograph, a firstsensitogram S_(refo) when the exposure time is set for a reference timet_(refo) ;

(g2) making, by means of the same variable time sensitograph, qsensitograms S₁ to S_(q) for q different exposure times t_(i) ;

(g3) choosing a reference optical density DO_(refo), for exampleDO_(refo) =1

(g4) measuring, on each sensitogram, illumination steps Ech_(refo), Ech₁. . . Ech_(i) . . . Ech_(q) corresponding to the optical densityDO_(refo) =1

(g5) calculating the coefficient CNRT (t_(i)) by the equation: ##EQU3##said coefficients CNRT (t_(i)) being modelized in the form of ananalytical model:

    CNRT (t.sub.i)=A.sub.0 +A.sub.1 log t+A.sub.2 [log t].sup.2( 18)

For the operation (b), the reference lumination L_(ref) may bedetermined by various calibrations, for example by means of a detectorcell that measures the light emitted by the screen.

BRIEF DESCRIPTION OF THE DRAWINGS

Other objects, features and advantages of the present invention shallappear from the following description of the method according to theinvention and from a particular exemplary embodiment of the radiologysystem used to implement it, said description being made with referenceto the appended drawings, of which:

FIG. 1 is a block diagram of a radiology system enabling theimplementation of the method according to the invention,

FIG. 2 is a graph showing curves obtained by implementing a method ofcalibration used in the method according to the invention;

FIG. 3 is a graph showing a curve of variation of the coefficients ofnon-reciprocity CNRT as a function of the exposure time t;

FIG. 4 is a graph showing a curve of variation of the coefficients ofnon-reciprocity CNRD as a function of the inverse of the dose rate d,and

FIG. 5 is a graph showing curves of variation of the optical density ofa radiographic film as a function of the lumination.

DETAILED DESCRIPTION OF THE INVENTION

A radiology system to which the method, according to the invention, forthe automatic determination of the exposure time of an object 13 to beradiographed, can be applied comprises an X-ray source 11 such as anX-ray tube that gives an X-ray beam illuminating this object 13 and animage receiver 17 such as a film/screen couple that is positioned so asto receive the X-rays having crossed said object and that gives an imageof the object 13 after an appropriate period of exposure S anddevelopment of the film.

To implement the method of the invention, the system further includes adetection cell 12, that is placed behind the image receiver 17 in thecase of a radiographic film with an intensifier screen. This cell may beplaced in front of the receiver in the case of a film without anintensifier screen. The detection cell 12 enables the conversion of aphysical variable, characteristic of the X-radiation that has crossedthe object and the image receiver, such as the KERMA or the energyfluence, into a measurement signal L, for example of the electricaltype. The signal L, given by the detection cell 12, is applied to acircuit 16 which carries out an integration of the electrical signalduring a duration S of the exposure. The signal M that results from theintegration is a measurement of the radiation that has crossed theobject 13 during the duration S of the exposure.

The X-radiation source 11 is associated with a power supply 15 thatgives a variable high supply voltage V_(m) for the X-ray tube andincludes an instrument for the measurement of the anode current I ofsaid tube. In order to modify the duration of the exposure time S, thepower supply 15 and the X-ray tube include means to start the X-rayemission at a precise instant and to stop it after a variable duration Sthat is determined, as a function of the signal M given by the circuit16 and of the values of I, S and V_(m) and, more precisely, of the ratioM/I×S which is called the yield D and is computed by a device 18. Thevalues of the yield D are processed by a computer or microprocessor 19.A conventional display monitors the microprocessor.

The method according to the invention shall now be described in thecontext of a more general method which is that of the automaticdetermination of the period of exposure of a radiographic film, a methodthat is the object of U.S. Pat. No. 5,218,625.

The first operation of the method for the automatic determination of theexposure time consists of performing a calibration of the radiologysystem of FIG. 1 that leads to a function of estimation of thelumination experienced by the radiographic film. This calibration andthe function of estimation are described in the French patentapplication filed on the same date as the present application andentitled: METHOD FOR THE ESTIMATION AND CALIBRATION OF THE LUMINATIONRECEIVED BY A RADIOGRAPHIC FILM.

For a better understanding of the remaining part of the description, itshall be recalled that the method for estimating the lumination receivedby a radiographic film is based on calibration operations that result inthe definition of a function proportional to the dose rate of photons onto the film, called the film dose rate, and on a calibration that can beused to establish the relationship between the film dose rate functionand the lumination received by the film under fixed reference conditionsand results in a given blackening of the film. This latter calibrationshall be described in fuller detail hereinafter in the description.

The calibrations that enable a definition of a film dose rate functionare derived from a calibration method described in U.S. patentapplication Ser. No. 07/535,520 filed on Jun. 8, 1990 and entitled:METHOD FOR THE CALIBRATION OF A RADIOLOGICAL SYSTEM AND FOR THEMEASUREMENT OF THE EQUIVALENT THICKNESS OF AN OBJECT. This methodconsists of measuring the yield D of the cell for each standard at thechosen supply voltages V_(m), More precisely, with a first thicknessstandard E₁, a measurement of yield D_(1m) is made for each value V_(m)constituting a determined set. These values D_(1m) as a function of thevoltage V_(m) may be entered in a graph to obtain the points 21' of FIG.2. The measurements of yield D are made for another thickness standardE₂ and the values D_(2m), corresponding to the points 22' of FIG. 2, andso on successively, are obtained, to obtain the other series of points23', 24' and 25' corresponding respectively to the yields D_(3m) D_(4m)and D_(5m) and to the thicknesses E₃, E₄ and E₅.

It must be noted that, in FIG. 2, the yields D_(pm) have been entered aslogarithmic y-axis values while the supply voltages have been entered asx-axis values from 20 kilovolts to 44 kilovolts.

These series of points 21' to 25' are used to define the parameters ofan analytical model that describes the behavior of the yield D as afunction of the parameters V_(m) and E_(p) for a given configuration ofthe radiological system. This analytical model shall be written as:

    D=f (V.sub.m, E.sub.p)                                     (1)

The parameters of the analytical model may be adjusted by means ofstandard estimation tools such as the minimal mean square error method.

The curves 21 to 25 represent the value of the yield D given by theanalytical model represented by the expression:

    D=f (V.sub.m, E.sub.p)=exp [f.sub.1 (V.sub.m)+E.sub.p ×f.sub.2 (V.sub.m)]                                                (2)

in which f₁ (V_(m)) and f₂ (V_(m)) are second-degree polynomials, theexpression of which is given by:

    f.sub.1 (V.sub.m)=A.sub.0 +A.sub.1 V.sub.m +A.sub.2 V.sub.m.sup.2

    (V.sub.m)=B.sub.0 +B.sub.1 V.sub.m +B.sub.2 V.sub.m.sup.2

The inverse function of that expressed by the formula (2) enables E_(p)to be computed, if D and V_(m) are known, by using the followingformula: ##EQU4## it being known that f₂ (V_(m)) cannot get cancelledout for the current values of V_(m) because the yield D always dependson the thickness E_(p) at the voltages V_(m) considered.

In other words, to a pair of values (E_(p), V_(m)) there corresponds ameasurement of yield D, which makes it possible to determine E_(p) as afunction of V_(m) and D. During a radiological examination, ameasurement of yield D, which is done with a given supply voltage V_(m),makes it possible to determine an equivalent thickness expressed in theunits used for E_(p).

This calibration is performed twice with configurations of the radiologysystem that differ as regards the receiver 17. The first of thesecalibration operations is done with the receiver 17 without intensifierscreen. By the equation 1, a function f' is determined, giving rise toyield values of the cell 12 referenced D_(se) such as:

    D.sub.se =f' (V.sub.m, E.sub.p)                            (4)

and the inverse function:

    E.sub.p =g' (V.sub.m, D.sub.se)                            (5)

The second operation of the method consists of performing a secondcalibration provided with an intensifier screen with a receiver 17 andthen a series of yield values D_(c) is obtained and, as above, thefunction f" is determined such that:

    D.sub.c =f" (V.sub.m, E.sub.p)                             (6)

and the inverse function

    E.sub.p =g" (V.sub.m, D.sub.c)                             (7)

From the above two calibration operations, a function D_(f) is deducedrepresenting the yield on the film such that:

    D.sub.f =D.sub.se -D.sub.c

that is

    D.sub.f =f' (V.sub.m, E.sub.p)-f' (V.sub.m, E.sub.p)       (8)

This function D_(f) does not take account of the modification of thespectrum of the X-radiation due to the additional filtration between theintensifier screen and the detection cell 12 that comes, for example,from the output face of the cartridge containing the film/screen couple.To take account of it, E_(p) in the equation (8) is replaced by (E_(p)-sup.filter) where sup.filter is the thickness equivalent to theradiographed object corresponding to this filtration. This equivalentthickness is obtained by placing, for example, in the beam 14, an objectequivalent to this filtration and by using the calibrated functiondetermining the equivalent thickness g' or g" according to theconfiguration of the machine.

Since the product D_(f) ×I×t is proportional to the energy absorbed inthe intensifier screen during a duration t and for an anode current I,the quantity D_(f) ×I, referenced film dose rate, is proportional to thedose rate of incident photons on the film and is expressed in the unitsof measurement of the signal of the detector cell 12. This relationshipof proportionality is verified all the more efficiently as the number oflight photons emitted by the intensifier screen is itself proportionalto the energy absorbed. If the number of light photons emitted by thescreen meets another relationship as a function of the energy absorbed,this other relationship must be applied to D_(f) ×I to obtain the filmdose rate.

A final calibration consists of linking the above-described electricalfunctions to a value of the blackening of the film, namely to an opticaldensity, that is to be obtained at the end of the exposure. This valueis chosen by the practitioner as a function of the film/screen couple,the type of diagnosis, the part of the patient's body to be examined andhis usual practices in examining radiographs. This choice makes itpossible to determine the reference lumination, referenced L_(ref),namely the lumination that must be received by the film, under fixedreference conditions, to arrive at a degree of blackening such as this.The method used to determine L_(ref) shall be described here below.

These calibration operations are not performed at each radiologicalexamination of an object or a patient, but only once in a while to takeaccount of the variations in the characteristics of the radiology systemin the course of time, notably variations such as the ageing of theX-ray tube. The results of these operations are recorded in the memoryof the microprocessor 19 in the form of functions represented by theequations 4 to 8. This means that the microprocessor 19 is capable ofcomputing E_(p) if it knows D_(c) and can then compute D_(f).

During the radiological examination of the patient, the method accordingto the invention further consists in performing the following main stepsof (or operations for):

(e1) positioning the object or patient to be radiographed,

(e2) triggering the start of the exposure by the practitioner,

(e3) measuring the yield D_(c) a certain time t' after the start of theexposure,

(e4) calculating the equivalent thickness from the measurement of yieldD_(c),

(e5) calculating the yield D_(f) at the film,

(e6) estimating the lumination received by the film since the start ofthe exposure,

(e7) calculating the lumination remaining to be acquired to obtain thechosen blackening,

(e8) calculating estimated mA.s remaining to be delivered in the X-raytube to obtain the chosen blackening,

(e9) measuring the mA.s, referenced mAs_(mes), delivered as the case maybe since the start of the exposure or since the preceding measurement,

(e10) stopping the X-radiation when the mAs_(mes) are greater than orequal to the mA.s computed or, if not, a return to the operation (e3).

It must be noted that the term "lumination" is applied to the product ofthe quantity of light received, for example the illumination EC of thesensitive surface, by the duration of exposure.

The operation (e3) consists of measuring the integrated value D given bythe device 18 at a certain time t' after the start of the exposure, itbeing known that the integrator 16 has been reset at zero either, as thecase may be, at the start of the exposure or after the last measurement.The integration time t' corresponds, as the case may be, to the timethat has elapsed since the start of the exposure or to the time that haselapsed since the last measurement.

The operation (e4) is performed by the microprocessor 19 from the firstcalibration of the radiology system as described here above: it isgoverned by the equation (7); a value E₁ of the equivalent thickness isthen obtained.

It must be observed that, for the second iteration of the method and forthe following ones, it is not necessary to perform the operation (e4) tothe extent that the estimation of the equivalent thickness has beensufficiently precise during the first iteration. The operation (e5)consists of computing the yield of the film D_(f1) corresponding to thethickness E₁ in using the function defined by the equation (8), whichmakes it possible to take account, notably, of the influence of thescreen of the receiver. This operation has been described briefly hereabove.

The operation (e6) consists of estimating the lumination L_(f) receivedby the film from the start of the exposure in applying the followingequation:

    L.sub.f =L.sub.am +D.sub.f1 ×δmA.s             (9)

This is an equation in which L_(am) is the lumination received by thefilm before the operation (e3) and δmA.s is the number of mA.s deliveredin the tube during the time t' and is defined by the product of the tubecurrent I by the integration time S.

The operation (e7) consists of computing the lumination remaining to beacquired L_(ra) to obtain the chosen blackening; it is determined by theequation:

    L.sub.ra =L.sub.ref -L.sub.f                               (10)

The operation (e8) consists of computing the mA.s remaining to bedelivered to obtain the chosen blackening which is given by theequation:

    mAs.sub.r =L.sub.ra /D.sub.f1                              (11)

It is then possible to deduce the number of mA.s delivered during thecomputations, referenced mAs_(c). Then, the mA.s that actually remain tobe acquired, referenced mAs_(ra), are defined by:

    mAs.sub.ra =mAs.sub.r -mAs.sub.c                           (12)

where

    mAs.sub.c =I×t.sub.c                                 (13)

with t_(c) being the time taken for the computations.

The operation (e10) consists of making a choice: either to stop theexposure or to continue it according to the value of the mAs remainingto be delivered or, again, the exposure time still to elapse, or torecompute the estimation of the estimated value of the end-of-exposuretime.

The end-of-exposure criterion could be the following:

If the value:

    Dif (mA.s)=mAs.sub.ra -mAs.sub.mes                         (15)

is nil or below a fixed value Val₀, the microprocessor 19 stops theX-radiation by action on the power supply 15. If not, the operation (e3)is returned to.

It is possible to envisage an additional test on the value of theexposure time still to elapse t_(rc) defined by the relationship:##EQU5##

This additional test consists of not modifying the value of theestimation mAs_(ra) should t_(rc) be smaller than a value t₀. Then theend of exposure terminates in an open loop through the continuance ofonly the end-of-exposure operations, namely the decrementation of thenumber of mA.s delivered and the stopping of the exposure when thisnumber becomes smaller than or equal to zero. A possible value of t₀ isa value substantially equal to the time interval between twomeasurements corresponding to the operation (e3). Thus, in this case,the operation (e10) comprises two tests:

a first test on mAs_(ra) to decide whether or not the exposure isstopped,

then a test on t_(rc) to decide whether to undertake a new estimation ofthe mAs remaining to be delivered or whether the value mAs_(ra) willremain fixed until the end of the exposure. In the latter case, theend-of-exposure test will be done periodically with the value mAs_(ra).

Besides, the operations for estimating the time still to elapse and thatof the interruption of exposure may be separated in order to furtherrefine the precision of the exposer. Thus, the method may be split up asfollows: a task T.E. designed to estimate the mA.s remaining to bedelivered before the end of the exposure and a task T.C. forinterrupting the exposure. These are two independent tasks that occur inparallel.

The task T.E. for estimating the mA.s still to be delivered isconstituted by the operations (e3) to (e8) to which there is added anoperation (e'9) of conversion of the mA.s into a signal in the units ofthe cell 12 such that:

    CE.sub.target =mAs.sub.ra ×D.sub.c                   (16)

This task of estimation T.E. is renewed periodically during theexposure, for example at the instants t₁, t₂, . . . t_(n) which areinstants of measurement separated by a period that is at least equal tothe computation time t_(c). At the end of the task of estimation T.E.,the target value CE_(target) of the task of interruption T.C. isupdated. This updating should take account of the signal received by thedetector cell 12 between the instant of measurement at the start of theoperation (e3) and the instant when the value CE_(target) is updated atthe end of the operation T.C.

The task of interrupting (T.C.) the exposure is one that consists indecrementing a given value (or target) as a function of the signalactually received by the cell 12. This task interrupts the exposure assoon as the value CE_(target) becomes smaller than or equal to Val₀,equal to zero for example.

Thus, the working of the task T.C. can be summarized in the followingsteps of :

(f1) measuring the integrated signal M_(m) by the cell 12 after acertain time t_(TC) ;

(f2) decrementing of this value to the target value: (CE_(target)-M_(m))

(f3) stopping the exposure when (CE_(target) -M_(m)) is lower than Val₀if not return to (f1).

The method that has just been described works accurately to the extentthat there is no deviation from the law of reciprocity for the receiver17 and the detection cell 12. If this is not the case, the operations(e6) and (e8) must be supplemented to take account of it and acoefficient of correction has to be determined by particularmeasurements and computations. This coefficient of correction isintroduced into the equations (9) and (11) where the lumination andyield of the film come into play.

It is thus that the formulas (9) and (11) become:

    L.sub.f =L.sub.am +D.sub.f1 ×δmA.s/CNRD (film dose rate)(9') ##EQU6##

    with film dose rate=D.sub.f1 ×I                      (17)

CNRD is the function representing the effect of non-reciprocityexpressed as a function of the dose rate of photons on the film.

The function CNRD is obtained by a method of calibration that is theobject of the present patent application. This method consists, first ofall, of determining the coefficients of non-reciprocity of the film as afunction of the duration of exposure t_(i), said coefficients beingreferenced CNRT (t_(i)). This function CNRT is determined experimentallyand may be represented by an analytical function.

More precisely, the method consists of the determination, for variousvalues IR_(i) of the intensity of the radiation, of the value t_(i) ofthe time of exposure needed to obtain a fixed optical density DO_(refo)of the film, for example DO_(refo) =1, and in the reading of the valuesgiven by the integrator circuit 16 for the different exposure timest_(i), namely values that shall be called M (t_(i)).

These values are compared with a reference value M (t_(ref)), which is,for example, the value corresponding to an exposure time of one second,in computing the ratio ##EQU7## It is this ratio that determines thecoefficient of non-reciprocity in time CNRT (t_(i)) for the exposuretime t_(i).

Another way to determine the coefficients CNRT (t_(i)) shall bedescribed further below.

These coefficients CNRT (t_(i)) are related to one another as a functionof the exposure time by the curve of FIG. 3 in the case, for example ofan optical density DO_(refo) =1 and a reference exposure time t_(ref) =1second. This curve shows that the lumination needed to achieve thedesired optical density increases with the exposure time. It is thusthat, in this example, the ratio between the energies for the twoexposure times of 50 ms and 6,5 s is of the order of 1,6.

The curve of FIG. 3 may be modelized by means of a function having theform:

    CNRT (t.sub.i)=A.sub.0 +A.sub.1 log t+A.sub.2 [log t].sup.2(18)

the parameters A₀, A₁ and A₂ being estimated from the measurement pointsby a least error squares method of estimation.

In principle, the Schwarzschild effect that is taken into account in theequations (9') and (11') could be modelized by the function CNRT. Thevalue of using the function CNRD indexed in dose rate is that it ispossible to take account of the variations of the anode current. Hence,an automatic exposer that uses the function CNRD according to theequations (9') and (11') has, for example, the advantage that the tubecan work in decreasing load. To go from the time-indexed coefficientsCNRT (t) to the rate-indexed coefficients CNRD (d), it is necessary totake account of the fact that the coefficients CNRT (t) have beendetermined by measurements with variable exposure times under conditionswhere the values of the photon dose rate on the film are not necessarilyknown. If the film dose rate d_(i) is measured for each exposure timet_(i), the value of the coefficient CNRD (d_(i)) for d_(i) will be equalto that of the coefficient CNRT (t_(i)) for the corresponding exposuretime t_(i) according to the relationship:

    CNRD (d.sub.i)=CNRT (t.sub.i)                              (19)

These different values of CNRD (d_(i)) are related to one another by acurve (FIG. 4) as a function of the reciprocal 1/d of the dose rate.This curve may be modelized by means of a function having the form:

    CNRD (d)=A'.sub.0 +A'.sub.1 log 1/d+A'.sub.2 [log 1/d]     (20)(20)

It may be the case that the values d_(i) are not given by thecalibration, especially because they are expressed in the measurementunit of the cell 12 which is not necessarily the one used in thecalibration. Thus, in general, the values d_(i) must be linked to theknown values t_(i) by the relationship:

    L.sub.ref ×CNRT (t.sub.i)=d.sub.i ×t.sub.i     (21)

or again: ##EQU8##

It is recalled here that L_(ref) is the lumination received by the filmunder fixed and known radiological conditions when the film attains agiven blackening and when the non-reciprocity effect is corrected.

To finalize the definition of the function CNRD, there remains themethod used to assess the reference lumination to be explained.

This method is described in the above-mentioned patent application,entitled: METHOD FOR THE ESTIMATION AND CALIBRATION OF THE LUMINATIONRECEIVED BY A RADIOGRAPHIC FILM.

The reference lumination depends on the optical density to be obtainedon the film. To determine this lumination, the first step is to make asensitogram of the type of film used, then a shot must be taken underdetermined radiological conditions with a known thickness standard.

These determined radiological conditions are, for example,

a reference optical density DO_(refo) chosen as a function of thepractitioner's usual practices, for example DO_(refo) =1

a thickness standard E₀,

a supply voltage V₀,

a value of the exposure time t₀,

a value of the product I₀ ×t₀,

For this shot, the optical density DO_(m) as well as the values M₀, I₀,t₀ are measured. This makes it possible to compute the equivalentthickness E_(p) by means of the formula (7). The yield D_(f) on the filmis then computed by means of the formula (6): this makes it possible tocompute the lumination received by the film L_(film) by the formula:

    L.sub.film =D.sub.f ×I.sub.0 ×t.sub.0          (23)

The reference optical density DO_(refo) makes it possible to compute theillumination step corresponding to DO_(refo) on the sensitometric curveof the film used, (FIG. 5), this curve having been plotted by means of asensitograph and a densitometer. This makes it possible to take accountof the characteristics of the developing machine that is used. The curveis recorded, for example, in the form of a function in themicroprocessor 19 (FIG. 1).

The optical density measured DO_(m) enables the computation of themeasurement step Ech_(m) which is the value of the illumination stepcorresponding to DO_(m) on the sensitometric curve (FIG. 5).

With the values L_(film) of the lumination on the film, the referencestep Ech_(ref) and the measurement step Ech_(m), it is possible tocompute the reference lumination L_(ref) to obtain the optical densityDO_(refo) by using the equation that defines the change in scale betweenthe lumination and the illumination step of the x-axis of thesensitometric curve (FIG. 5), that is: ##EQU9## From this equation (24),we derive: ##EQU10##

The sensitometric constant K corresponds to the scale chosen for theillumination steps. The value L_(ref) depends on t₀ through L_(film) bythe equations (23) and (25). Thus, the value L_(ref) is sensitive to thenon-reciprocity effects of the film. To correct the influence ofnon-reciprocity on the value of L_(ref), it is enough to use, in theequation (23), the value L_(film) defined by: ##EQU11##

This reference lumination L_(ref) is the one that must be used in theequation (10) to obtain the reference optical density DO_(refo) , forexample DO_(refo) =1, and the formula (25) shows that it depends,notably, on the difference between the reference step and themeasurement step. The knowledge of the lumination received by the filmprovides for knowing d_(i) by the application of the formula (22) andfor deducing CNRD (d_(i)) therefrom by the formula (20).

For an optical density of the radiographic film other than DO_(refo) =1,the above-described operations have to be repeated so as to determinethe new values of CNRT (t_(i)) and of L_(ref).

In order to simplify these operations, the coefficients CNRT (t_(i)) maybe obtained by performing the following steps of:

(g1) making, by means of a variable time sensitograph, a firstsensitogram S_(refo) (FIG. 5) when the exposure time is set for areference time t_(refo) ;

(g2) making, by means of the same variable time sensitograph, qsensitograms S₁ to S_(q) (FIG. 5) for q different exposure times t_(i) ;

(g3) choosing a reference optical density DO_(refo), for exampleDO_(refo) =1

(g4) measuring, on each sensitogram, the illumination step Ech_(refo),Ech₁ . . . Ech_(i) . . . Ech_(q) corresponding to the optical densityDO_(refo) =1

(g5) calculating the coefficient CNRT (t_(i)) by the equation: ##EQU12##

If the practitioner decides to work at a different optical density, itis proposed, in order to avoid the above-described calibration, to usethe optical density deliberately corrected for the blackening DO_(cvn).Then, the reference lumination L_(ref), used in the equation (10) shouldbe replaced by the corrected lumination L_(cvn) which is expressed by:

    L.sub.cvn =L.sub.ref ×exp[CVN/Γ×P×Log(10)](27)

where

CVN is the deliberate correction of blackening expressed by a wholenumber from -10 to +10 for example,

P is the elementary step in optical density, for example 0,1,

Γ is the slope of the linear part of the sensitometric curve (FIG. 5).

The method that has just been described shows that its implementationcalls for a certain number calibrations that are, briefly, thefollowing:

(a) the calibration of the radiological system so as to determine theanalytical models

    D.sub.se =f' (V.sub.m, E.sub.p)                            (4)

with cartridge without screen and

    D.sub.c =f"(V.sub.m, E.sub.p)                              (6)

E_(p) =g"(V_(m), D_(c)) (7)

with cartridge and screen;

The difference D_(f) =(D_(se) -D_(c)) (equation (8)) will make itpossible to deduce the yield absorbed by the screen;

(b) the calibration of the film so as to determine the law ofnon-reciprocity CNRT (t) expressed as a function of the time; this lawwill be used to determine the law of non-reciprocity CNRD (d) expressedas a function of the dose rate;

(c) the calibration of the reference lumination L_(ref).

When these different calibrations have been performed, the methodcomprises the steps of:

(d) choosing, by the practitioner, the blackening value or of the valueof the deliberate correction of blackening so as to determine the targetlumination L_(cvn) that should be received by the film under fixedreference conditions to arrive at the chosen blackening (or opticaldensity). The lumination L_(cvn) is computed from the equation (27)where the lumination L_(ref) is determined by the calibration (c) andthe equations (25) and (26);

(e1) positioning the object to the radiographed,

(e2) triggering the start of the exposure by the practitioner

(e3) measuring after a time t' the yield D_(c1) at the cell (12);

(e4) measuring the equivalent thickness E₁ by the equation (7);

(e5) calculating the yield D_(f1) at the film for the thickness E₁ bythe equation (8);

(e6) calculating the lumination L_(f), received by the film, by theequation;

    L.sub.f =L.sub.am +D.sub.f1 ×δmA.s/CNRD (film dose rate)(9')

(e7) calculating the lumination L_(ra) remaining to be acquired toobtain the blackening (or optical density) chosen by the equation

    L.sub.ra =L.sub.cvn -L.sub.f                               (10')

(e8) calculating the estimated mA.s remaining to be delivered mAs_(ra)to obtain the blackening (or optical density) by the equation:

    mAs.sub.ra =L.sub.ra /D.sub.f1 ×CNRD (film dose rate)(11')

(e9) measuring the mA.s delivered since the start of the operation (e3);

(e10)--stopping the exposure when the mA.s measured in (e9) are equal toor greater than mAs_(ra).

or returning to the operation (e3) when the mA.s measured in (e9) areless than mAs_(ra).

The description of the method that has just been given corresponds to acertain configuration of the radiology system. Should it be possible forthis system to assume several configurations involving, for example, thechoice of:

the material of the anode

the dimensions of the focus,

the spectrum modifying filter,

the collimation,

the presence or absence of a diffusion-preventing screen,

the type of image receiver,

the type of detection cell,

it is necessary to perform calibrations (a), (b) and (c) for each ofthese configurations. The number of these calibrations may be reduced bytaking account of the similarities of behavior from one configuration toanother, as described for the calibration (a) in U.S. patent applicationSer. No. 07/535 520 filed on Jun. 8, 1990.

When the practitioner implements the method, he defines theconfiguration, and the characteristics of this configuration aretransmitted to the microprocessor (19) so that the latter uses thecorresponding models.

The method according to the invention has been described in itsapplication to a receiver 17 of the film/screen couple type. It can alsobe implemented in the case of a receiver 17 having only a film sensitiveto X-radiation. With such a film, the calibrations of the operations (a)and (b) become:

(a') the calibration of the radiological system so as to determine theanalytical model

    D'.sub.f =f"'(V.sub.m, E.sub.p)                            (30)

with the film as the image receiver.

In the unfolding of the method, the modifications are as follows:

(e3) becomes (e'3): measuring after a time t' the yield D'_(f1) at thecell 12;

(e4) and (e5) are eliminated and

the steps (e6) to (e8) are modified in the following way:

(e'6) calculating the lumination L' _(f) received by the film by theequation:

    L'.sub.f =L.sub.am +D'.sub.f1 ×δmA.s/CNRD (film dose rate)(9")

(e'7) calculating the lumination L'_(ra) remaining to be acquired toobtain the blackening (or optical density) chosen by the equation

L'_(ra) =L_(cvn) -L'_(f) (10")

(e'8) calculating the estimated mA.s remaining to be delivered mAs_(ra)to obtain the blackening (or optical density) by the equation:

    mAs'.sub.ra =L'.sub.ra /D'.sub.f1 ×CNRD (film dose rate)(11")

The other operations (e9) and the ones that follow remain unchanged.

Besides, it must be noted that the sensitograph may, in this case, be ofthe X-ray emission type. Furthermore, with a receiver such as this,having no intensifier screen, the detection cell 12 may be placed eitherbehind the receiver 17, as in the case of the film/screen type receiver,or before the receiver 17 if the energy of the radiation allows it.

What is claimed is:
 1. A method for determining the functionrepresenting the effect of non-reciprocity of a radiographic film in asystem of radiology designed to examine an object that includes an X-raytube, the supply voltage V of which may assume various values V_(m),with continuous or discrete variation, said X-ray tube emitting an X-raybeam in the form of pulses of variable duration t_(i) towards the objectto be examined, a receiver of the X-radiation that has crossed theobject to form an image of said object, a cell for the detection of theX-rays that have crossed the object to be examined, that enables theconversion of a physical variable, characterizing the X-ray beam, into ameasurement signal L, an integrator circuit that integrates themeasurement signal L for the duration t_(i) and gives a signal M, and adevice to compute the yield D given by the ratio of M to the productI×t_(i) (or mA.s) of the anode current I of the tube by the duration tiof the exposure, wherein said method includes the following steps:(a)determining the coefficients of non-reciprocity CNRT (t_(i)) of the filmexpressed in exposure time t_(i) for an optical density DO_(refo) ofsaid film; (b) determining the reference lumination L_(ref) received bysaid film; (c) calculating the photon dose rates d_(i) on said film bythe formula: ##EQU13## (d) determining the coefficients ofnon-reciprocity CNRD (d_(i)) expressed in photon dose rate d_(i) by theapplication of the formula:

    CNRD (d.sub.i)=CNRT (t.sub.i)

wherein the step (a) comprises the following steps: (a1) modifying thetube heating current so as to obtain different values of said current,(a2) reading the values M (t_(i)) given by the integrator circuit fordifferent exposure times (t_(i)) so as to obtain an optical density DO₁of the film, (a3) calculating the ratio ##EQU14## which gives thecoefficient CNRT (t_(i)) with M (t_(ref)) the value M (t_(i)) for t_(i)=t_(ref).
 2. A method for determining the function representing theeffect of non-reciprocity of a radiographic film in a system ofradiology designed to examine an object that includes an X-ray tube, thesupply voltage V of which may assume various values V_(m), withcontinuous or discrete variation, said X-ray tube emitting an X-ray beamin the form of pulses of variable duration t_(i) towards the object tobe examined, a receiver of the X-radiation that has crossed the objectform an image of said object, a cell for the detection of the X-raysthat have crossed the object to be examined, that enables the conversionof a physical variable, characterizing the X-ray beam, into ameasurement signal L, an integrator circuit that integrates themeasurement signal L for the duration t_(i) and gives a signal M, and adevice to compute the yield D given by the ratio of M to the productI×t_(i) (or mA.s) of the anode current I of the tube by the durationt_(i) of the exposure, wherein said method includes the followingsteps:(a) determining the coefficients of non-reciprocity CNRT (t_(i))of the film expression in exposure time t_(i) for an optical densityDO_(refo) of said film; (b) determining the reference lumination L_(ref)received by said film; (c) calculating the photon dose rates d_(i) onsaid film by the formula: ##EQU15## (d) determining the coefficients ofnon-reciprocity CNRD (d_(i)) expressed in photon dose rate d_(i) by theapplication of the formula:

    CNRD (d.sub.i)=CNRT (t.sub.i)

wherein the step (a) includes the following operations: (a1) making, bymeans of a variable time sensitograph, a first sensitogram S_(refo) whenthe exposure time is set for a reference time t_(refo) ; (a2) making, bymeans of the same variable time sensitograph, q sensitograms S₁ to S_(q)for q different exposure times t_(i) ; (a3) choosing a reference opticaldensity DO_(refo) ; (a4) measuring, on each sensitogram, theillumination step Ech_(refo) ; Ech₁ . . . Ech_(i) . . . Ech_(q)corresponding to the optical density DO_(refo) ; (a5) calculating thecoefficient CNRT (t_(i)) by the equation: ##EQU16##
 3. A methodaccording to claims 1 or 2, wherein the step (a) further includes thefollowing step of:determining the function of modelization of thecoefficients CNRT (t_(i)) such that:

    CNRT (t.sub.i)=A.sub.0 +A.sub.1 log t+A.sub.2 [log t].sup.2


4. A method according to any of the claims 1 or 2, wherein the step (b)consists in measuring said lumination L_(ref) by a detector cell.
 5. Amethod according to any of the claims 1 or 2, wherein the referencelumination L_(ref) is determined by a calibration method that includesthe following steps should the image receiver be formed by at least oneintensifier screen and a film sensitive to the light from thisscreen:taking a shot under determined radiological conditions for areference optical density DO_(ref), a thickness standard E₀, a supplyvoltage V₀, an exposure time t₀ and a value of the product I₀ ×t₀ ;measuring the yield D₀ ; calculating the equivalent thickness E_(p0) bythe formula:

    E.sub.p0 =g" (V.sub.0, D.sub.0)

calculating the yield D_(f0) on the film by the formula:

    D.sub.f0 =f' (V.sub.0, E.sub.0)-f" (V.sub.0, E.sub.p0)

calculating the luminance L_(film), on the film by the formula:

    L.sub.film =D.sub.f0 ×I.sub.0 ×t.sub.0

calculating the illumination step Ech_(ref) corresponding to thereference optical density DO_(refo) by means of the sensitometric curve;measuring the optical density DO_(m) of the shot obtained and thecomputation of the illumination step Ech_(m) by means of thesensitometric curve; calculating the reference lumination L_(ref) by theformula: ##EQU17##

    with K=2/log.sub.10 (2)


6. A method according to claim 5 wherein, for calculating the yieldD_(f0) on the film by the equation D_(f0), the equivalent thicknessE_(p0) is replaced by (E_(p0) -sup.filter), (sup.filter) being theequivalent thickness due to the additional filtration resulting from theattentuation between the intensifier screen and the detection cell.
 7. Amethod according to claim 5, when the image receiver is formed by a filmsensitive to X-radiation and when the detection cell is placed before orbehind said film, wherein the yield D_(f0) on the film is computed bythe formula:

    D'.sub.f0 =f"' (V.sub.m, E.sub.p)


8. A method according to claim 7 wherein, in the equation D'_(f0), thethickness E_(p) is replaced by (E_(p) -sup.filter), (sup.filter) beingthe equivalent thickness due to the additional filtration resulting fromthe attenuation between the receiver film and the detection cell.
 9. Amethod according to claim 3, wherein, the luminance on the film iscalculated by the formula: ##EQU18##
 10. A method for determining thefunction representing the effect of non-reciprocity of a radiographicfilm in a system of radiology designed to examine an object thatincludes an X-ray tube, comprising the steps of:supplying voltage to thetube at various values, V_(m) ; exposing an object to X-ray beams in theform of pulses of variable duration, t_(i) ; exposing film to X-raybeams after passage through the object; subjecting an X-ray radiationdetector cell to tile beams for converting beam energy, passed throughthe object, into a measurement signal L; integrating the signal L fortile duration ti and generating a resulting signal M; measuring thecurrent I supplied to an anode of the X-ray tube; calculating the yieldD from the ratio of tile signal M to the product of I×t_(i) during aninterval of exposure; determining the coefficient of non-reciprocityCNRT (t_(i)) of the film as a function of exposure time t_(i) for anoptical density DO_(refo) of the film; calculating the photon dose ratesd_(i), as a function of a reference illumination on the film (L_(ref))by the formula: ##EQU19## and determining the coefficients ofnon-reciprocity CNRD (d_(i)) as a function photon dose rate d_(i) by theformula:

    CNRD (d.sub.i)=CNRT (t.sub.i).


11. A method according to claim 10 further comprising the stepsof:determining the function of modelization of the coefficients CNRD (d)such that--

    CNRD (d)=A'.sub.0 +A'.sub.1 log 1/d+A'.sub.2.